Numerical Estimation of the Complex Refractive Indexes by the Altitude Depending on Wave Frequency in the Ionized Region of the Earth Atmosphere for Microwaves Information and Power Transmissions

Abstract

Abstract-The phase and group refractive indexes of microwaves in the ionosphere region of the earth atmosphere are very important for both the researching theoretical problems and practical problems in wireless information transmission (WIT) and wireless power transmission (WPT). So far, there have been many attempts devoted to discussing and determining characterizations of earth atmosphere's ionosphere region including the refractive indexes of microwaves concerning their velocities in ionized region, unfortunately due to the complicated features of the ionosphere region leading to research task facing many challenges. Up to recent, there is still a lack of systematic numerical data of complex refractive index by altitude depending on high frequencies of the electromagnetic waves in the ionosphere region. This paper outlines some theoretical analyses and discussions of some theoretical aspects of the complex refractive index in atmosphere's ionized region more in detail. Based on conductivities data and the complex relative permittivity by altitude determined previously, the numerically estimated data of complex refractive indexes by the altitude from 100 km up to 1000 km at the different frequencies are also shown and discussed.

Electromagnetic Field Solutions in an Isotropic Medium With Weakly-Random Fluctuations in Time and Some Applications in the Electrodynamics of the Ionosphere

“…The case with constants and μ leads to the standard form of the equations for electromagnetic wave propagation in a steady homogeneous medium. More generally, Equations (17) and (18) are obtained in any configuration where…”

“…In the present paper, we examine Equations (17) and 18in a two-dimensional domain described by rectangular coordinates x and z. We consider a bounded domain in the…”

“…In an isotropic medium where the electric and magnetic fields satisfy Eqs. (17) and (18) respectively, each component E of the electric field vector E and each component H of the magnetic field vector H satisfy, respectively,…”

“…Var{ double their wavelengths as a result of the nonlinear interactions between the electromagnetic field and the medium [18]. Taking x 1 = 0, x 2 = λ x and r = −1.5 [17], we obtain an induced average EMF = 45 kV and a standard deviation SD{EMF} = 1 kV, leading to a 95% confidence interval EMF = EMF ± 2SD{EMF} = (45 ± 2) kV. And so, the overall average electric field vector is E =xE x +ẑE z =x EMF/λ x +ẑ EMF/λ z = [(0.38 ± 0.01)x + (0.50 ± 0.02)ŷ] mV/m as can be observed in the ionosphere [23].…”

“…As a second example of the application of formula (61), we consider large scale travelling ionospheric disturbances (LSTIDs) or electromagnetohydrodynamic disturturbances (EMHD) with horizontal wavelength λ x = 1200 km and vertical wavelength λ z = 1000 km observed in the ionospheric F region generated by the electric field (53) and the magnetic field (60) as a result of a magnetic storm [7,24], make the approximations η 1 ≈ 2(2π/λ x ) and η 2 ≈ 2(2π/λ z ), and take x 1 = 0, x 2 = λ x and r = −1.5 as before [17]. We then obtain the induced EMF = (500 ± 22) kV as might be observed in the ionosphere [23].…”